Elementary Real Analysis: A Practical Introduction provides a robust foundation for success in real analysis, presenting traditional material in an accessible, engaging manner with the support of clearly outlined learning objectives and exercises.
Organized into three well-designed sections, the book begins with a comprehensive review of prerequisite knowledge. Section I includes chapters such as "Sets," "Mathematical Statements," and "Proof Methods", which establish the essential language and techniques of advanced mathematics. Section II explores the properties of real numbers, integers, and functions, each accompanied by a wealth of exercises that encourage exploration and practice. The final section delves into advanced topics such as sequences, continuity, and differentiation, culminating in a synthesis of concepts that prepares students for rigorous mathematical analysis.
Whether used in a classroom or for self-directed learning, Elementary Real Analysis: A Practical Introduction is a vital companion for students seeking an introduction to real analysis, bridging the gap between basic principles and advanced mathematical concepts with clarity and precision.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Preface - p. ix 7. Part 1: Elementary topics - p. P1 8. Chapter 1: Sets - p. 3 9. Chapter 2: Properties of real numbers - p. 9 10. Chapter 3: Properties of integers - p. 21 11. Chapter 4: Functions and relations - p. 29 12. Part 2: Advanced topics - p. P2 13. Chapter 5: Sequences Part 1 - p. 47 14. Chapter 6: Continuity and differentiation - p. 75 15. Chapter 7: Sequences Part 2 - p. 89 16. Chapter 8: Putting it all together - p. 103 17. Chapter 9: Riemann integration Part 1 - p. 139 18. Chapter 10: Riemann integration Part 2 - p. 171 19. Appendix A: Mathematical statements - p. 189 20. Appendix B: Proof methods - p. 197 21. Index - p. 201
Elementary Real Analysis: A Practical Introduction provides a robust foundation for success in real analysis, presenting traditional material in an accessible, engaging manner with the support of clearly outlined learning objectives and exercises.
Organized into three well-designed sections, the book begins with a comprehensive review of prerequisite knowledge. Section I includes chapters such as "Sets," "Mathematical Statements," and "Proof Methods", which establish the essential language and techniques of advanced mathematics. Section II explores the properties of real numbers, integers, and functions, each accompanied by a wealth of exercises that encourage exploration and practice. The final section delves into advanced topics such as sequences, continuity, and differentiation, culminating in a synthesis of concepts that prepares students for rigorous mathematical analysis.
Whether used in a classroom or for self-directed learning, Elementary Real Analysis: A Practical Introduction is a vital companion for students seeking an introduction to real analysis, bridging the gap between basic principles and advanced mathematical concepts with clarity and precision.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Preface - p. ix 7. Part 1: Elementary topics - p. P1 8. Chapter 1: Sets - p. 3 9. Chapter 2: Properties of real numbers - p. 9 10. Chapter 3: Properties of integers - p. 21 11. Chapter 4: Functions and relations - p. 29 12. Part 2: Advanced topics - p. P2 13. Chapter 5: Sequences Part 1 - p. 47 14. Chapter 6: Continuity and differentiation - p. 75 15. Chapter 7: Sequences Part 2 - p. 89 16. Chapter 8: Putting it all together - p. 103 17. Chapter 9: Riemann integration Part 1 - p. 139 18. Chapter 10: Riemann integration Part 2 - p. 171 19. Appendix A: Mathematical statements - p. 189 20. Appendix B: Proof methods - p. 197 21. Index - p. 201
